One of the first articles I ever wrote on medium discussed what I had always considered to be my favorite integral, the golden integral is, however, a new contender. My favorite integral aka I don’t care what your teacher told you, π ≠ 22/7. By calculating a very simple integral we can see that π ≠ 22/7 regardless of what we were told in school.stephenwithaphd.medium.com Let’s quickly recap. The golden ratio, ϕ, is the positive solution to the equation

As some of you may have noticed, I have not published for about a month. This was because, as the title suggests, I took a break from math. This was something I had been planning to do for a while, and when the opportunity arose over December I just took…

Let’s play a game. I have 5 levels of surd-themed questions below. The game is, as you would expect, to start on level 1 (question 1) and work your way to level 5 (question 5). There is no time limit. The only rule is that you can only progress if…

Have you ever asked yourself how to calculate an irrational exponent? For example, what is the value of

Continuing my series on the interesting questions my students have asked me, all of which you can now find here, in this article we look at a teacher versus student challenge. This was the final week of the semester and it was to be me against the class in a…

I have always enjoyed questions that involve factorials. The first puzzle I can remember being given in a maths class required the teacher to explain the factorial symbol to us. This was my first introduction to proper mathematical notation outside of your basic everyday notation, and it was the first…

I recently went searching for some non-calculator Olympiad questions for a beginners' training session and I came across 4 interesting candidates. These each require nothing more than some basic manipulation tricks, but each of these tricks is a very useful tool to have in our toolbox. Here are the four…

Continuing my series on the interesting questions my students have asked me, in this article we look at an interesting algebraic problem. This problem was posed by some students who are training for the math Olympiads. They claim it came from a past Olympiad paper, but I am unsure which…

You will not see me write about a lot of geometry puzzles for the simple fact that I am not good at them! They often require seeing the “object(s)” in question in just the right way, after which the solution generally becomes relatively easy. This is a skill I simply…